On the Observability of the Collision Matrix
Though the expression “S matrix” was coined by Heisenberg , the idea of epitomizing the collision process by specifying only the final state of the collision products, i.e., the concept of the collision matrix, was first advanced by Wheeler . He was seeking—and achieving—a concise description of the collision process. Heisenberg’s motivation for introducing the collision matrix was his belief, at the time he wrote his paper, that the detailed structure of the system during the collision is unobservable; only the final state, when the collision products are outside one another’s range of influence, can be ascertained experimentally. Heisenberg expected the S matrix to become, in one form or another, a substitute for the concepts of field theory, since the quantities with which that theory deals are of doubtful observability. This idea is, of course, the basis of much modern thought, embodied in dispersion theory, which will not, however, be the subject of this essay. Rather, we will go one step further in the direction that motivated Heisenberg, to query the extent to which the elements of the collision matrix are observable.
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- 1.W. Heisenberg, Z. Physik,120, 673 (1943). Heisenberg’s attribution of a fundamental nature to the collision matrix is reflected in much of modern theoretical physics that has centered on dispersion theory. The literature of this is too large to be described in a footnote. The effort to define spacetime points on the basis of collision theory has attracted perhaps less attention than it deserves. The papers originating this development are M. L. Goldberger and K. M. Watson, Phys. Rev.,127, 2284 (1962), and M. Froissart, M. L. Goldberger, and K. M. Watson, Phys. Rev.,131, 2820 (1963). Heisenberg’s ideas on the fundamental nature of the collision matrix have been taken up, extended, and modified on the epistemological level, principally by H. P. Stapp. See his forthcoming article, “S-matrix Interpretation of Quantum Theory,” in The Physical Review.Google Scholar
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